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DTSTAMP:20260404T110140Z
UID:1648728000@ist.ac.at
DTSTART:20220331T140000
DTEND:20220331T150000
DESCRIPTION:Speaker: Christopher Frei\nhosted by Tim Browning\nAbstract: Th
 e Hasse norm principle is a local-global principle for norm forms in exten
 sions of number fields. It holds for all cyclic extensions\, but may fail 
 in general. We present a useful criterion for the validity of the Hasse no
 rm principle in the case of abelian extensions\, which is essentially a re
 formulation of a theorem of Tate. When combined with counting techniques o
 riginally due to Mäki\, Wright and Matchett Wood\, this criterion allows 
 us to study the distribution of extensions satisfying the Hasse norm princ
 iple in families with fixed abelian Galois group\, ordered by discriminant
  and conductor\, with qualitatively different results depending on which o
 f these two invariants one uses. When counting by conductor\, the criterio
 n can also be used to prove an asymptotic formula for extensions with fixe
 d abelian Galois group in which an arbitrary finite set of elements of the
  base field have to be norms. In particular\, we show that such extensions
  always exist. This is joint work with Dan Loughran and Rachel Newton. Sin
 ce then\, non-analytic proofs of this last result were found. An algebro-g
 eometric proof was given by Harpaz and Wittenberg\, and in joint work with
  Rodolphe Richard we have used again the criterion mentioned above to give
  a class-field theoretic proof.We will first survey these results and tech
 niques and then look at some aspects in more detail. 
LOCATION:Heinzel Seminar Room (I21.EG.101)\, Office Building West\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Christopher Frei: Quantitative and constructive results on norms in
  abelian extensions
URL:https://talks-calendar.ista.ac.at/events/3525
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